AQA Physics A (2540)

Fields and Further Mechanics

A2 Module questions

Student name:1.A toy locomotive of mass 0.50kg is initially at rest on a horizontal track. The locomotive is powered by a twisted rubber band which, as it unwinds, exerts a force which varies with time as shown in the table.time/s0.01.02.03.04.05.06.07.08.0

force/N0.200.180.150.120.100.080.050.020.00

(a)(i)On the graph paper plot a graph of force against time for the rubber band power source. Time/s on the x-axis and force /N on the y-axis.(ii)State what is given by the area between the graph and the time axis............................................................................................................................(4)(b)The rubber band is wound up and released to power the locomotive. Use your graph to show that the speed of the locomotive 8.0s after the twisted rubber band is released is l.6ms1. Ignore the effects of air resistance and energy losses due to friction.....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2) (c)8.0s after release the locomotive collides with and couples to a toy truck, initially at rest, which has a mass of 1.50kg.(i)Calculate the speed of the coupled locomotive and truck after collision....................................................................................................................................................................................................................................................... (ii)Calculate the combined kinetic energy of the locomotive and truck immediately after collision....................................................................................................................................................................................................................................................... (iii)Show, with the aid of a calculation, whether or not the collision is elastic..................................................................................................................................................................................................................................................................................................................................................................................(5)(Total 11 marks)2.(a)(i)Give an equation showing how the principle of conservation of momentum applies to the colliding snooker balls shown in the diagram.

...........................................................................................................................(ii)State the condition under which the principle of conservation of momentum applies.......................................................................................................................................................................................................................................................(3)(b)A trolley, A, of mass 0.25 kg and a second trolley, B, of mass 0.50 kg are held in contact on a smooth horizontal surface. A compressed spring inside one of the trolleys is released and they then move apart. The speed of A is 2.2 m s1.(i)Calculate the speed of B.................................................................................................................................................................................................................................................................................................................................................................................. (ii)Calculate a minimum value for the energy stored in the spring when compressed..................................................................................................................................................................................................................................................................................................................................................................................(4)(c)The rotor blades of a helicopter sweep out a cross-sectional area, A. The motion of the blades helps the helicopter to hover by giving a downward velocity, , to a cylinder of air, density . The cylinder of air has the same cross-sectional area as that swept out by the rotor blades.Explaining your reasoning,(i)derive an expression for the mass of air flowing downwards per second, and.................................................................................................................................................................................................................................................................................................................................................................................(ii)derive an expression for the momentum given per second to this air.......................................................................................................................................................................................................................................................(iii)Hence show that the motion of the air results in an upward force, F, on the helicopter given by

F = A2..................................................................................................................................................................................................................................................................................................................................................................................(5)(d)A loaded helicopter has a mass of 2500 kg. The area swept out by its rotor blades is 180m2. If the downward flow of air supports 50% of the weight of the helicopter, what speed must be given to the air by the motion of the rotor blades when the helicopter is hovering? Take the density of air to be 1.3 kg m3................................................................................................................................................................................................................................................................................................................................................................................................................(3)(Total 15 marks)3.A machine gun fires bullets of mass 0.050 kg at a speed of 450 m s1(a)Calculate the momentum of a bullet as it emerges from the gun......................................................................................................................................(2)(b)(i)Explain why a soldier holding the machine gun will experience a force from the gun whilst it is firing bullets.......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

...........................................................................................................................

(ii)The maximum steady horizontal force a soldier can exert on the gun is 150 N.Calculate the maximum number of bullets the gun can fire every second.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(4)(Total 6 marks)4.(a)State the principle of conservation of linear momentum for two colliding bodies................................................................................................................................................................................................................................................................................................................................................................................................................(2) (b)

A bullet of mass 0.010 kg travelling at a speed of 200 m s1 strikes a block of wood of mass 0.390 kg hanging at rest from a long string. The bullet enters the block and lodges in the block. Calculate(i)the linear momentum of the bullet before it strikes the block,...........................................................................................................................(ii)the speed with which the block first moves from rest after the bullet strikes it.......................................................................................................................................................................................................................................................(4)(c)During the collision of the bullet and block, kinetic energy is converted into internal energy which results in a temperature rise.(i)Show that the kinetic energy of the bullet before it strikes the block is 200 J............................................................................................................................(ii)Show that the kinetic energy of the combined block and bullet immediately after the bullet has lodged in the block is 5.0 J............................................................................................................................ (iii)The material from which the bullet is made has a specific heat capacity of250 J kg1 K1. Assuming that all the lost kinetic energy becomes internal energy in the bullet, calculate its temperature rise during the collision..................................................................................................................................................................................................................................................................................................................................................................................(5)(d)The bullet lodges at the centre of mass G of the block. Calculate the vertical height h through which the block rises after the collision................................................................................................................................................................................................................................................................................................................................................................................................................(2)(Total 13 marks)5.(a)Collisions can be described as elastic or inelastic. State what is meant by an inelastic collision........................................................................................................................................................................................................................................................................... (b)A ball of mass 0.12 kg strikes a stationary cricket bat with a speed of 18 m s1. The ball is in contact with the bat for 0.14 s and returns along its original path with a speed of 15ms1.Calculate(i)the momentum of the ball before the collision,...................................................................................................................................................................................................................................................... (ii)the momentum of the ball after the collision,......................................................................................................................................................................................................................................................(iii)the total change of momentum of the ball,......................................................................................................................................................................................................................................................(iv)the average force acting on the ball during contact with the bat,...................................................................................................................................................................................................................................................... (v)the kinetic energy lost by the ball as a result of the collision,......................................................................................................................................................................................................................................................(6)(Total 7 marks)6.The diagram represents part of an experiment that is being used to estimate the speed of an air gun pellet.

The pellet which is moving parallel to the track, strikes the block, embedding itself. The trolley and the block then move along the track, rising a vertical height, h.(a)Using energy considerations explain how the speed of the trolley and block immediately after it has been struck by the pellet, may be determined from measurements of h. Assume frictional forces are negligible....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3) (b)The following data is collected from the experiment

mass of trolley and block0.50 kgmass of pellet0.0020 kgspeed of trolley and block immediately after impact0.40 m s1 Calculate(i)the momentum of the trolley and block immediately after impact,...................................................................................................................................................................................................................................................... (ii)the speed of the pellet just before impact..................................................................................................................................................................................................................................................................................................................................................................................(4)(c)(i)State what is meant by an inelastic collision.................................................................................................................................................................................................................................................................................................................................................................................. (ii)Use the data from part (b) to show that the collision between the pellet and block is inelastic..................................................................................................................................................................................................................................................................................................................................................................................(4)(Total 11 marks)7.A girl kicks a ball along the ground at a wall 2.0 m away. The ball strikes the wall normally at a velocity of 8.0 m s1 and rebounds in the opposite direction with an initial velocity of6.0 m s1. The girl, who has not moved, stops the ball a short time later.(a)Explain why the final displacement of the ball is not 4.0 m................................................................................................................................................................................................................................................................................................................................................................................................................

.....................................................................................................................................(1) (b)Explain why the average velocity of the ball is different from its average speed................................................................................................................................................................................................................................................................................................................................................................................................................

.....................................................................................................................................(2)(c)The ball has a mass of 0.45 kg and is in contact with the wall for 0.10 s. For the period of time the ball is in contact with the wall,(i)calculate the average acceleration of the ball....................................................................................................................................................................................................................................................... (ii)calculate the average force acting on the ball............................................................................................................................ (iii)state the direction of the average force acting on the ball............................................................................................................................(5)(Total 8 marks)8.(a)State two quantities that are conserved in an elastic collision.quantity 1: ..................................................................................................................quantity 2: ..................................................................................................................(2) (b)A gas molecule makes an elastic collision with the walls of a gas cylinder. The molecule is travelling at 450 m s1 at right angles towards the wall before the collision.(i)What is the magnitude and direction of its velocity after the collision?......................................................................................................................................................................................................................................................(ii)Calculate the change in momentum of the molecule during the collision if it has a mass of 8.0 1026 kg.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(4) (c)Use Newtons laws of motion to explain how the molecules of a gas exert a force on the wall of a container.

You may be awarded additional marks to those shown in brackets for the quality of written communication in your answer...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(4)(Total 10 marks) 9.A chemical centrifuge consists of two test-tube holders which can be spun round in a horizontal circular path at very high speed as shown. The centrifuge runs at a steady speed of 3000 revolutions per minute and the test-tube holders are horizontal.

(i)Calculate the angular speed of the centrifuge in rad s1........................................................................................................................................................................................................................................................................ (ii)Calculate the magnitude of the acceleration at a point on the centrifuge 95 mm from the axis of rotation......................................................................................................................................................................................................................................................................... (iii)State the direction of the acceleration in part (ii).....................................................................................................................................(Total 5 marks)10.

A 150 g mass is attached to one end of a light inextensible string and the other end of the string is fixed at a point P as shown in the diagram above. The mass is held at point A so that the string is taut and horizontal. The mass is released so that it moves freely along a circular arc of 250 mm radius.

When the string moves through the vertical position, the mass is at point B. Neglecting the effect of air resistance, calculate(i)the kinetic energy of the mass,...............................................................................................................................................................................................................................................................................................................................................................................................................(ii)the velocity of the mass,.......................................................................................................................................................................................................................................................................... (iii)the centripetal force acting on the mass,..........................................................................................................................................................................................................................................................................(iv)the tension in the string...........................................................................................................................................................................................................................................................................(Total 6 marks)11.

A simple pendulum consists of a bob of mass m on the end of a light string of length l. The bob is released from rest at X when the string is horizontal. When the bob passes through Y its velocity is and the tension in the string is T. Which one of the following equations gives the correct value of T?AT = mgBT = CT + mg = DT mg = (Total 1 mark)12.A body is in simple harmonic motion of amplitude 0.50 m and period 4 seconds. What is the speed of the body when the displacement of the body is 0.30 m?A0.10 m s1B0.15 m s1C0.20 m s1D0.40 m s1(Total 1 mark) 13.A girl of mass 40 kg stands on a roundabout 2.0 m from the vertical axis as the roundabout rotates uniformly with a period of 3.0 s. The horizontal force acting on the girl is approximatelyAzero.B3.5 102 N.C7.2 102 N.D2.8 104 N.(Total 2 marks)14.For a particle moving in a circle with uniform speed, which one of the following statements is incorrect?AThe velocity of the particle is constant.BThe force on the particle is always perpendicular to the velocity of the particle.CThere is no displacement of the particle in the direction of the force.DThe kinetic energy of the particle is constant.(Total 2 marks)15.

A model car moves in a circular path of radius 0.8 m at an angular speed of rad s1.What is its displacement from point P, 6 s after passing P?AzeroB1.6 mC0.47 mD1.6 m(Total 2 marks)16.A particle of mass m moves in a circle of radius r at uniform speed, taking time T for each revolution. What is the kinetic energy of the particle?A

B

C

D

(Total 2 marks)17.A fairground roundabout makes nine revolutions in one minute. What is the angular speed of the roundabout?A0.15 rad s1B0.34 rad s1C0.94 rad s1D2.1 rad s1(Total 2 marks)18.(a)State what is meant by(i)a free vibration,...................................................................................................................................................................................................................................................... (ii)a forced vibration.......................................................................................................................................................................................................................................................(2) (b)A car and its suspension can be treated as a simple mass-spring system. When four people of total weight 3000 N get into a car of weight 6000 N, the springs of the car are compressed by an extra 50 mm.(i)Calculate the spring constant, k, of the system.......................................................................................................................................................................................................................................................(ii)Show that, when the system is displaced vertically and released, the time period of the oscillations is 0.78 s..................................................................................................................................................................................................................................................................................................................................................................................(3) (c)The loaded car in part (b) travels at 20 ms1 along a road with humps spaced 16 m apart.(i)Calculate the time of travel between the humps....................................................................................................................................................................................................................................................... (ii)Hence, state and explain the effect the road will have on the oscillation of the car..................................................................................................................................................................................................................................................................................................................................................................................(3)(Total 8 marks)19.(a)A vibrating system which is experiencing forced vibrations may show resonance.Explain what is meant byforced vibrations ...........................................................................................................................................................................................................................................resonance................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3)(b)(i)Explain what is meant by damping....................................................................................................................................................................................................................................................... (ii)What effect does damping have on resonance?......................................................................................................................................................................................................................................................(2)(Total 5 marks)20.A spring, which obeys Hookes law, hangs vertically from a fixed support and requires a force of 2.0 N to produce an extension of 50mm. A mass of 0.50kg is attached to the lower end of the spring. The mass is pulled down a distance of 20mm from the equilibrium position and then released.(a)(i)Show that the time period of the simple harmonic vibrations is 0.70 s....................................................................................................................................................................................................................................................... (ii)Sketch the displacement of the mass against time, starting from the moment of release and continuing for two oscillations. Show appropriate time and distance scales on the axes.

(5)(b)The mass-spring system described in part (a) is attached to a support which can be made to vibrate vertically with a small amplitude. Describe the motion of the mass-spring system with reference to frequency and amplitude when the support is driven at a frequency of(i)0.5 Hz,.................................................................................................................................................................................................................................................................................................................................................................................(ii)1.4 Hz..................................................................................................................................................................................................................................................................................................................................................................................(3)(Total 8 marks)21.Which one of the following statements always applies to a damping force acting on a vibrating system?AIt is in the same direction as the acceleration.BIt is in the same direction as the displacement.CIt is in the opposite direction to the velocity.DIt is proportional to the displacement.(Total 1 mark)22.A simple pendulum and a mass-spring system are taken to the Moon, where the gravitational field strength is less than on Earth. Which line, A to D, correctly describes the change, if any, in the period when compared with its value on Earth?period of pendulumperiod of mass-spring system

Adecreasedecrease

Bincreaseincrease

Cno changedecrease

Dincreaseno change

(Total 2 marks) 23.A body moves with simple harmonic motion of amplitude A and frequency .

What is the magnitude of the acceleration when the body is at maximum displacement?AzeroB42Ab2CAb2D

(Total 2 marks) 24.

(a)When a 200 g mass is suspended from a spring, as in Figure 1, it produces an extension of 3.5 cm. Calculate the spring constant, k, for this spring...........................................................................................................................................................................................................................................................................(2) (b)A spring identical to that in part (a) is joined to the lower end of the original one and a 500 g mass is suspended from the combination, as shown in Figure 2.(i)State the value of the new spring constant for this combination of two springs............................................................................................................................(ii)When the 500 g mass is displaced it performs small vertical oscillations. Calculate the number of oscillations made in one minute.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3)(Total 5 marks) 25.A mass M hangs in equilibrium on a spring. M is made to oscillate about the equilibrium position by pulling it down 10 cm and releasing it. The time for M to travel back to the equilibrium position for the first time is 0.50 s. Which line, A to D, is correct for these oscillations?amplitude/cmperiod/s

A101.0

B102.0

C202.0

D201.0

(Total 2 marks)26.To celebrate the Millennium in the year 2000, a footbridge was constructed across the River Thames in London. After the bridge was opened to the public it was discovered that the structure could easily be set into oscillation when large numbers of pedestrians were walking across it.(a)What name is given to this kind of physical phenomenon, when caused by a periodic driving force?.....................................................................................................................................(1)(b)Under what condition would this phenomenon become particularly hazardous? Explain your answer...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(4) (c)Suggest two measures which engineers might adopt in order to reduce the size of the oscillations of a bridgemeasure 1 ................................................................................................................................................................................................................................................measure 2 ................................................................................................................................................................................................................................................(2)(Total 7 marks) 27.A simple pendulum consists of a 25 g mass tied to the end of a light string 800 mm long. The mass is drawn to one side until it is 20 mm above its rest position, as shown in the diagram. When released it swings with simple harmonic motion.

(a)Calculate the period of the pendulum...........................................................................................................................................................................................................................................................................(2) (b)Show that the initial amplitude of the oscillations is approximately 0.18 m, and that the maximum speed of the mass during the first oscillation is about 0.63 m s1............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... (4) (c)Calculate the magnitude of the tension in the string when the mass passes through the lowest point of the first swing.....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2)(Total 8 marks) 28.When the length of a simple pendulum is decreased by 600 mm, the period of oscillation is halved. What is the original length of the pendulum?A800mmB1000mmC1200mmD1400mm(Total 2 marks) 29.An electric motor in a machine drives a rotating drum by means of a rubber belt attached to pulleys, one on the motor shaft and one on the drum shaft, as shown in the diagram below.

(a)The pulley on the motor shaft has a diameter of 24 mm. When the motor is turning at 50revolutions per second, calculate(i)the speed of the belt,............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(ii)the centripetal acceleration of the belt as it passes round the motor pulley........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(5) (b)When the motor rotates at a particular speed, it causes a flexible metal panel in the machine to vibrate loudly. Explain why this happens..........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2)(Total 7 marks) 30.What is the angular speed of a point on the Earths equator?A7.3 105 rad s1B4.2 103 rad s1C2.6 101 rad s1D15 rad s1(Total 2 marks) 31.(a)A body is moving with simple harmonic motion. State two conditions that must be satisfied concerning the acceleration of the body.

condition 1 ..........................................................................................................................................................................................................................................................condition 2 ................................................................................................................................................................................................................................................(2) (b)A mass is suspended from a vertical spring and the system is allowed to come to rest.When the mass is now pulled down a distance of 76 mm and released, the time taken for 25oscillations is 23 s.

Calculate(i)the frequency of the oscillations,.......................................................................................................................................................................................................................................................... (ii)the maximum acceleration of the mass,..........................................................................................................................................................................................................................................................(iii)the displacement of the mass from its rest position 0.60 s after being released. State the direction of this displacement.....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(6)(c)

Figure 1

Figure 1 shows qualitatively how the velocity of the mass varies with time over the first twocycles after release. (i)Using the axes in Figure 2, sketch a graph to show qualitatively how the displacementof the mass varies with time during the same time interval.

Figure 2(ii)Using the axes in Figure 3, sketch a graph to show qualitatively how the potential energy of the mass-spring system varies with time during the same time interval.

Figure 3(4)(Total 12 marks)32.

A small loudspeaker emitting sound of constant frequency is positioned a short distance above a long glass tube containing water. When water is allowed to run slowly out of the tube, the intensity of the sound heard increases whenever the length l (shown above) takes certain values.(a)Explain these observations by reference to the physical principles involved.

You may be awarded marks for the quality of written communication in your answer..............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(4) (b)With the loudspeaker emitting sound of frequency 480 Hz, the effect described in part (a) is noticed first when l = 168 mm. It next occurs when l = 523 mm.

Use both values of l to calculate(i)the wavelength of the sound waves in the air column,......................................................................................................................................................................................................................................................(ii)the speed of these sound waves.......................................................................................................................................................................................................................................................(4)(Total 8 marks)33.(a)Give an equation for the frequency, f, of the oscillations of a simple pendulum in terms of its length, l, and the acceleration due to gravity, g...........................................................................................................................................................................................................................................................................

State the condition under which this equation applies...........................................................................................................................................................................................................................................................................(2) (b)The bob of a simple pendulum, of mass 1.2 102 kg, swings with an amplitude of 51mm. It takes 46.5 s to complete 25 oscillations. Calculate(i)the length of the pendulum,....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... (ii)the magnitude of the restoring force that acts on the bob when at its maximum displacement........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(6)(Total 8 marks)34.(a)State, in words, Newtons law of gravitation...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2)(b)Some of the earliest attempts to determine the gravitational constant, G, were regarded as experiments to weigh the Earth. By considering the gravitational force acting on a mass at the surface of the Earth, regarded as a sphere of radius R, show that the mass of the Earth is given by

M = ,where g is the value of the gravitational field strength at the Earths surface.....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2)(c)In the following calculation use these data.

radius of the Moon= 1.74 106 mgravitational field strength at Moons surface= 1.62 N kg1mass of the Earth M= 6.00 1024 kggravitational constant G= 6.67 1011 Nm2 kg2

Calculate the mass of the Moon and express its mass as a percentage of the mass of the Earth..........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3)(Total 7 marks)35.The gravitational field strength at the surface of a planet, X, is 19 N kg1.(a)(i)Calculate the gravitational potential difference between the surface of X and a point 10 m above the surface, if the gravitational field can be considered to be uniform over such a small distance....................................................................................................................................................................................................................................................... (ii)Calculate the minimum amount of energy required to lift a 9.0 kg rock a vertical distance of 10m from the surface of X.......................................................................................................................................................................................................................................................(iii)State whether the minimum amount of energy you have found in part (a)(ii) would be different if the 9.0 kg mass were lifted a vertical distance of 10 m from a point near the top of the highest mountain of planet X. Explain your answer..................................................................................................................................................................................................................................................................................................................................................................................(3) (b)Calculate the gravitational field strength at the surface of another planet, Y, that has the same mass as planet X, but twice the diameter of X.....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2)(Total 5 marks)36.Take the acceleration due to gravity, gE, as 10 m s2 on the surface of the Earth.The acceleration due to gravity on the surface of the Moon is. An object whose weight on Earth is 5.0 N is dropped from rest above the Moons surface. What is its momentum after falling for 3.0s?A2.5 kg m s1B6.2 kg m s1C15 kg m s1D25 kg m s1(Total 1 mark)37.Both gravitational and electric field strengths can be described by similar equations written in the form

a =.(a)Complete the following table by writing down the names of the corresponding quantities, together with their SI units, for the two types of field.symbolgravitational fieldquantity SI unitelectrical fieldquantity SI unit

agravitationalfield strength

bm F1

c

d

(4) (b)Two isolated charged objects, A and B, are arranged so that the gravitational force between them is equal and opposite to the electric force between them.(i)The separation of A and B is doubled without changing their charges or masses. State and explain the effect, if any, that this will have on the resultant force between them....................................................................................................................................................................................................................................................... (ii)At the original separation, the mass of A is doubled, whilst the charge on A and the mass of B remain as they were initially. What would have to happen to the charge on B to keep the resultant force zero?......................................................................................................................................................................................................................................................(3)(Total 7 marks)38.(a)The graph shows how the gravitational potential varies with distance in the region above the surface of the Earth. R is the radius of the Earth, which is 6400 km. At the surface of the Earth, the gravitational potential is 62.5 MJ kg1

Use the graph to calculate(i)the gravitational potential at a distance 2R from the centre of the Earth,...........................................................................................................................(ii)the increase in the potential energy of a 1200kg satellite when it is raised from the surface of the Earth into a circular orbit of radius 3R..................................................................................................................................................................................................................................................................................................................................................................................(4)(b)(i)Write down an equation which relates gravitational field strength and gravitational potential............................................................................................................................ (ii)By use of the graph in part (a), calculate the gravitational field strength at a distance 2R from the centre of the Earth.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(iii)Show that your result for part (b)(ii) is consistent with the fact that the surface gravitational field strength is about 10 N kg1.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(5)(Total 9 marks) 39.The following data refer to two planets.radius/kmdensity/kg m3

planet P80006000

planet Q160003000

The gravitational field strength at the surface of P is 13.4 N kg1. What is the gravitational field strength at the surface of Q?A 3.4 N kg1B13.4 N kg1C53.6 N kg1D80.4 N kg1(Total 1 mark) 40.The gravitational potential difference between the surface of a planet and a point P, 10 m above the surface, is 8.0 J kg1. Assuming a uniform field, what is the value of the gravitational field strength in the region between the planets surface and P?A0.80 N kg1B1.25 N kg1C8.0 N kg1D80 N kg1(Total 2 marks)41.A satellite is in orbit at a height h above the surface of a planet of mass M and radius R. What is the velocity of the satellite?A

B

C

D

(Total 2 marks) 42.The mass of the nucleus of an isolated copper atom is 63 u and it carries a charge of +29 e. The diameter of the atom is 2.3 1010 m.

P is a point at the outer edge of the atom.

(a)Calculate(i)the electric field strength at P due to the nucleus,.................................................................................................................................................................................................................................................................................................................................................................................(ii)the gravitational potential at P due to the nucleus..................................................................................................................................................................................................................................................................................................................................................................................(5) (b)Draw an arrow on the above diagram to show the direction of the electric field at the point P.(1)(Total 6 marks) 43.(a)Complete the table of quantities related to fields. In the second column, write an SI unit for each quantity. In the third column indicate whether the quantity is a scalar or a vector.quantitySI unitscalar or vector

gravitational potential

electric field strength

magnetic flux density

(3)(b)(i)A charged particle is held in equilibrium by the force resulting from a vertical electric field. The mass of the particle is 4.3 109 kg and it carries a charge of magnitude 3.2 1012 C. Calculate the strength of the electric field.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(ii)If the electric field acts upwards, state the sign of the charge carried by the particle.......................................................................................................................(3)(Total 6 marks) 44.(a)The Moons orbit around the Earth may be assumed to be circular. Explain why no work is done by the gravitational force that acts on the Moon to keep it in orbit aroundthe Earth.

You may be awarded marks for the quality of written communication provided in youranswer.................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3) (b)Give an example of a situation where a body(i)travels at constant speed but experiences a continuous acceleration,......................................................................................................................................................................................................................................................(ii)experiences a maximum acceleration when its speed is zero.......................................................................................................................................................................................................................................................(2)(Total 5 marks) 45.The Global Positioning System (GPS) is a system of satellites that transmit radio signals which can be used to locate the position of a receiver anywhere on Earth.

(a)A receiver at sea level detects a signal from a satellite in a circular orbit when it is passing directly overhead as shown in the diagram above.(i)The microwave signal is received 68 ms after it was transmitted from the satellite. Calculate the height of the satellite.......................................................................................................................................................................................................................................................(ii)Show that the gravitational field strength of the Earth at the position of the satellite is 0.56 N kg1.mass of the Earth=6.0 1024 kgmean radius of the Earth=6400 km.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(4)(b)For the satellite in this orbit, calculate(i)its speed,............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(ii)its time period........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(5)(Total 9 marks) 46.(a)Explain what is meant by the gravitational potential at a point in a gravitational field.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2)(b)Use the following data to calculate the gravitational potential at the surface of the Moon.

mass of Earth = 81 mass of Moonradius of Earth = 3.7 radius of Moongravitational potential at surface of the Earth = 63 MJ kg1................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... (3) (c)Sketch a graph on the axes below to indicate how the gravitational potential varies with distance along a line outwards from the surface of the Earth to the surface of the Moon.(3) (Total 8 marks) 47.(a)(i)Define electric field strength, and state whether it is a scalar quantity or a vector quantity............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. (ii)Complete the diagram below to show the electric field lines in the region around two equal positive point charges. Mark with a letter N the position of any point where the field strength is zero.

(6)(b)Point charges A, of +2.0 nC, and B, of 3.0 nC, are 200 mm apart in a vacuum, as shown by the figure. The point P is 120 mm from A and 160 mm from B.

(i)Calculate the component of the electric field at P in the direction AP.................................................................................................................................................................................................................................................................................................................................................................................. (ii)Calculate the component of the electric field at P in the direction PB..................................................................................................................................................................................................................................................................................................................................................................................(iii)Hence calculate the magnitude and direction of the resultant field at P.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(6) (c)(i)Explain why there is a point X on the line AB in part (b) at which the electric potential is zero............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. (ii)Calculate the distance of the point X from A.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(4)(Total 16 marks) 48.(a)Figure 1 shows a pair of parallel metal plates, A and B, fixed vertically 20 mm apart with a potential difference of 1500 V between them.

(i)Draw the electric field lines in the space between the plates and calculate the electric field strength at P.(ii)Sketch a graph showing the potential at different points in the space between the plates.

(5)(b)Figure 2 shows a polystyrene ball of mass 5.0 104 kg suspended midway between the plates by a long insulating thread. The ball has a conducting surface and carries an initial charge of 3.0 nC.

(i)Calculate the force on the ball due to the electric field and hence show that the ball, when released from rest, will take a time of approximately 0.2 s to reach one conducting plate. State the direction of motion of the ball........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(ii)Explain why the ball will subsequently shuttle backwards and forwards between the plates.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(6)(c)The same charged ball described in part (b) is suspended at rest between the poles of a magnet. State the magnitude and direction of the force (if any) on the ball and explain your answer.............................................................................................................................................................................................................................................................................................................................................................................................................(2)(Total 13 marks)49.

A positive ion with a mass of 3.4 1026 kg and a charge of 3.2 1019 C is initially at rest at a point P, midway between two parallel conducting plates, A and B which are separated by 40 mm. The ion is accelerated and passes through a hole Q in plate B. It enters a magnetic field of uniform flux density 0.10 T at R. After following a circular path the ion leaves the field at S. Assume that the magnetic field is uniform everywhere within the dotted rectangle and that the space within the solid rectangle is evacuated.(a)(i)Calculate the electric field strength between the plates AB..................................................................................................................................................................................................................................................................................................................................................................................(ii)Calculate the force on the ion due to the electric field....................................................................................................................................................................................................................................................... (iii)Show that the speed of the ion just after it has passed through the hole at Q is3.1 105 ms1.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(5) (b)(i)State the direction of the magnetic field............................................................................................................................ (ii)Explain why the ion follows a circular path in the magnetic field.................................................................................................................................................................................................................................................................................................................................................................................. (iii)Show that the radius of the circular path is proportional to the momentum of the ion and calculate the value of the radius............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. (6) (c)Explain how, if at all, the trajectory would be different for an ion with a slightly greater mass but carrying the same charge................................................................................................................................................................................................................................................................................................................................................................................................................ (2)(Total 13 marks) 50.Which one of the following statements about electric potential and electric field strength is correct?AElectric potential is zero whenever the electric field strength is zero.BElectric field strength is a scalar quantity.CElectric potential is a vector quantity.DElectric potential due to a point charge varies as where r is the distance from the point charge.(Total 2 marks) 51.Two identical conducting spheres on insulating supports carry charges of magnitude Q and 2Q respectively. When separated by distance d, the electrostatic repulsive force is F. The spheres are made to touch and then restored to their original separation d. If there is no loss of charge what is the new force of repulsion?A

B

C

D

(Total 2 marks) 52.

The diagram shows two charges, +4 C and 16 C, 120 mm apart. What is the distance from the +4 C charge to the point between the two charges, where the resultant electric potential is zero?A24 mmB40 mmC80 mmD96 mm(Total 2 marks)53.Two parallel metal plates separated by a distance d have a potential difference V across them. What is the magnitude of the electrostatic force acting on a charge Q placed midway between the plates?

A

B

C

D

(Total 2 marks) 54.(a)For a capacitor of capacitance C, sketch graphs of charge, Q, and energy stored, E, against potential difference, V.

What is represented by the slope of graph A?..................................................................................................................................(3)(b)A capacitor of capacitance 0.68 F is charged to 6.0 V. Calculate(i)the charge stored by the capacitor,..............................................................................................................................................................................................................................................(ii)the energy stored by the capacitor...............................................................................................................................................................................................................................................(2)(Total 5 marks) 55.(a)A 2.0 F capacitor is charged through a resistor from a battery of emf 4.5 V. Sketch a graph on the axes below to show how the charge stored, Q, varies with the potential difference, V, across the capacitor during the charging process. Mark appropriate values on the axes of the graph.

(2)(b)(i)Show that the energy stored by a charged capacitor is given by E = QV........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................ (ii)Calculate the energy stored by the capacitor in part (a) when the potential difference across it is 1.5 V.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(5)(Total 7 marks) 56.A camera flashgun uses the discharge of a capacitor to provide the energy to produce a single flash. In a particular flashgun a 4700 F capacitor is initially charged from a 90 V supply.(a)Calculate(i)the charge stored by the capacitor when it is fully charged,...................................................................................................................................................................................................................................................... (ii)the energy stored by the fully-charged capacitor,......................................................................................................................................................................................................................................................(iii)the average current which flows if total discharge of the capacitor takes place effectively in 30 ms.......................................................................................................................................................................................................................................................(3) (b)During a partial discharge of the capacitor the potential difference between its terminals falls from 90 V to 80 V. Calculate the energy discharged to the flashgun........................................................................................................................................................................................................................................................................... (2)(Total 5 marks) 57.A parallel plate capacitor consists of two smooth square metal plates with sides of length0.35 m. The gap between the plates is filled completely with a sheet of mica of thickness 0.15mm. The plates of the capacitor are connected across the terminals of a 1.2 kV supply. Refer to the Data Sheet for any additional information.(a)Calculate(i)the magnitude of the charge on the capacitor,.......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(ii)the resistance of the mica sheet, i.e. the resistance between the plates.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(6) (b)When the capacitor is disconnected from the supply there is a leakage current through the mica sheet and the charge reduces to zero in about 3 hours. Calculate the mean current flowing during the loss of charge from the capacitor................................................................................................................................................................................................................................................................................................................................................................................................................(2) (c)Explain why there is a limit to the magnitude of the potential difference that may be applied between the plates of the capacitor.....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3)(Total 11 marks) 58.A student used a voltage sensor connected to a datalogger to plot the discharge curve for a4.7 F capacitor. She obtained the following graph.

Use data from the graph to calculate(a)the initial charge stored,.....................................................................................................................................(2) (b)the energy stored when the capacitor had been discharging for 35 ms,..........................................................................................................................................................................................................................................................................(3) (c)the time constant for the circuit,....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3) (d)the resistance of the circuit through which the capacitor was discharging................................................................................................................................................................................................................................................................................................................................................................................................................(2)(Total 10 marks)59.A 10 mF capacitor is charged to 10 V and then discharged completely through a small motor. During this process, the motor lifts a weight of mass 0.10 kg. If 10% of the energy stored in the capacitor is used to lift the weight, through what approximate height will the weight be lifted?A0.05 mB0.10 mC0.50 mD1.00 m(Total 2 marks) 60.(a)A capacitor is made from two parallel metal plates of the same area, separated by an air gap. It is connected across a battery of constant e.m.f.

The plates are moved further apart, maintaining the same area of overlap, whilst the battery remains connected. State and explain what change, if any, occurs to(i)the potential difference across the plates,........................................................................................................................... (ii)the capacitance of the capacitor,........................................................................................................................... (iii)the charge on each plate of the capacitor,...........................................................................................................................(iv)the energy stored by the capacitor............................................................................................................................(4) (b)A thunder cloud and the earth beneath it can be considered to form a parallel plate capacitor. The area of the cloud is 8.0 km2 and it is 0.75 km above the earth.(i)Calculate the energy stored if the potential difference between the cloud and the earth is 200 kV......................................................................................................................................................